It sounds like the harmless "Daring jumping spider," Phidippus audax, which is commonly found all over the United States. This small spider is black and furry with a couple white spots on its back. Four of it's anterior eyes are very large and you should be able to see them without a magnifying glass. The spider also has emerald green pedipalps. Without a location it's very hard to tell exactly what it could be. If the spider is not furry at all, I suggest staying away from it if you live in a tropical area as it could be poisonous.
What you've described sounds like a White-Spotted Jumping Spider, otherwise known as a Daring Jumping Spider or Phippus Audax; totally harmless to humans and also quite beneficial as they eat the more dangerous, venomous Spiders. If possible, keep her around. She won't hurt you unless you make her feel cornered and threatened.
My guess is that this spider you saw was either a Jumping Spider (quite possibly a Daring Jumping Spider) or a Parson Spider.
a type of jumping spider?
black hairy with white dots on its back
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the black widow heh heh heh.....
a redback spider
Phidippus audax
Sounds like a "Spotted Ground Swift Spider"http://www.geocities.com/brisbane_spiders/Corinnidae.htm
I just caught a spider that matches this description. After looking online, I think it may be a jumping spider from the family Salticidae. I believe that spider is Phidippus Audax a.k.a the Bold Jumping Spider.
There are many different kinds of spiders that are brown with white spots. To properly identify them, it helps to determine if the spots are in any particular pattern, the overall body shape of the spider, and where it is living. Such a spider may be a sic-spotted fishing spider, a bold jumping spider, or an orb-weaving garden spider.
A garden orb weaver probably
Brown Rectcluse Brown Rectcluse